New signing Philippe Coutinho marked his full Liverpool debut with a goal as Liverpool beat an understrength Swansea side with one eye on next week's Wembley final 5-0 at Anfield.

The 20-year-old scored the important second moments after the break following Steven Gerrard's first-half penalty. Jose Enrique, Luis Suarez and Daniel Sturridge, also from the spot, finished off the visitors who rarely looked interested in, or capable of, making a contest of it.

Brendan Rodgers, facing the club he left in the summer for the third time this season, began the week talking up what an important seven days lay ahead. But after a home defeat to West Brom and an away loss to Zenit St Petersburg in the Europa League, this game took on even more significance.

It was a match Liverpool effectively could not afford to do anything but win, although that only served to paper over the cracks which have been exposed recently. As emphatic as the scoreline was - incredibly securing a first win over a top-10 side this season - it only served to prove just how frustrating the Reds can be.

Earlier in the week they created as many if not more chances against the Baggies but failed to put any away. The same problem befell them in Russia, with a similar 2-0 defeat the outcome, but in some ways Swansea probably provided the ideal opposition for the Reds to end a five-match winless run.

Physically not intimidating, with a bigger prize on offer in seven days' time, they were also the perfect team for the slight and youthful-looking Coutinho to make his first start since an £8.5million move from Inter Milan late last month.

Swansea boss Michael Laudrup, with his thoughts on next weekend's Capital One Cup final, did his predecessor a huge favour by naming a weakened side, selecting only four of the team who beat QPR 4-1 last week and leaving out 15-goal striker Michu, captain Ashley Williams and Nathan Dyer.

Had Liverpool not beaten a side which was arguably not as strong as the one which defeated the Reds 3-1 in the League Cup in October, serious questions would have been asked.

After striker Roland Lamah's hopeful appeals for a handball against Glen Johnson were waved away by referee Howard Webb the match settled into a familiar and all-too-frustrating pattern for the hosts. England right-back Johnson planted a free header well wide, Gerrard drilled a free-kick into the wall and Suarez fired the rebound over, before the Uruguay international whipped a 25-yard free-kick just over the bar, where he also dispatched a dipping volley.

The chances continued to be created and not converted as Sturridge missed the target with a close-range header before the £12 million signing appeared to be brought down by Kyle Bartley. Referee Howard Webb saw nothing untoward but worse was to follow as Liverpool's other January arrival Coutinho stabbed the loose ball wide with the goal at his mercy

Webb was also unconvinced by Kemy Agustien's unnecessary challenge on Suarez close to the touchline but, fortunately for the home side, his assistant Mike Mularkey saw it differently and immediately flagged for a penalty. Gerrard, having failed from the spot in front of the Kop against West Brom, went for the opposite corner and succeeded in beating Michel Vorm for Liverpool's first goal.

Sturridge had one more chance before the break but having been put through by Suarez, his left-footed toe poke was blocked by the head of Bartley.

Swansea had shown little threat in the opening 45 minutes and any ideas they may have had about staging a comeback were snuffed out within 10 minutes of the restart. In truth, the 16 seconds it took Coutinho to skip through the visitors' defence and beat Vorm was all that was required.

However, a well-worked goal saw Enrique poke home Sturridge's pass before Suarez went past both Swansea centre-backs to fire home the fourth.

The persevering Sturridge was denied again by Vorm as the Reds ploughed forward almost at will with Swansea seemingly powerless to stop them or provide any effective response of their own. He finally got his goal but only courtesy of the generosity of Gerrard, who relinquished penalty duties when substitute Wayne Routledge handled.

Liverpool, who finished with 10 men after third and final substitute Fabio Borini went off with a painful-looking shoulder injury, have now scored 17 goals in their last five home games with only the two conceded against West Brom spoiling a perfect run at Anfield.

The key for Rodgers, as it has been for the entire season, is to find a way of ensuring this is not just another flash in the pan as his side moved to within nine points of fourth-placed Tottenham.